INTEGRAL CLOSURE OF A FILTRATION RELATIVE TO A NOETHERIAN MODULE

Let M be a Noetherian R-module. In this paper we will introduce the integral closure of a filtration F= {In} n≥0 relative to the Noetherian module M and prove some related results. The integral closure of a filtration F~= {In} n≥0 relative to M is a filtration and it has an interesting relationship with the integral closure of the filtration F= {I~n} n≥0, where I~n is the image of In under the natural ring homomorphism R → R/(AnnR(M)) for every n ≥ 0.